Optimal variable acceptance sampling plan for exponential distribution using Bayesian estimate under Type-I hybrid censoring

Year 2024, Volume: 53 Issue: 4, 1178 - 1195, 27.08.2024

Ashlyn Marıa Mathaı , Mahesh Kumar

https://doi.org/10.15672/hujms.1355348

Abstract

Acceptance sampling plans with censoring schemes are crucial for improving quality control by efficiently managing incomplete information. This approach improves cost and time effectiveness compared to traditional methods, providing a more accurate assessment of product quality. In this study, a variable acceptance sampling plan under Type-I hybrid censoring is designed for a lot of independent and identical units with exponential lifetimes using Bayesian estimation of the mean life. This novel approach diverges from conventional methods in acceptance sampling plans, which rely on maximum likelihood estimation and the minimization of Bayes risk. Bayesian estimation is obtained using both squared error loss and Linex loss functions. Under each method, a nonlinear optimization problem is solved to minimize the testing cost, and the optimal values of the plan parameters are determined. The proposed plans are illustrated using various numerical examples, with each plan presented in tables. The acceptance sampling plan using the squared error loss function proves to be more cost-effective than the plan using the Linex loss function. A comparative analysis of the proposed plans with existing work in the literature demonstrates that our cost is much lower than the cost of existing plans using maximum likelihood estimation. Additionally, a real-life case study is conducted to validate the approach.

Keywords

Acceptance sampling plan, Type-I hybrid censoring, exponential distribution, Bayesian estimate, squared error loss, Linex loss, Lindley’s approximation

References

• [1] M. Aslam, G.S. Rao and N. Khan, Single-stage and two-stage total failure-based groupsampling plans for the Weibull distribution under neutrosophic statistics, Complex Intell Syst 7, 891-900, 2021.
• [2] M. Aslam, G.S. Rao, N. Khan and L. Ahmad, Two-stage sampling plan using process loss index under neutrosophic statistics, Comm. Statist. Simulation Comput. 51 (6), 2831-2841, 2022.
• [3] P.N. Bajeel and M. Kumar, Optimal reliability test plan for a parallel system with co-variate information, in: Statistical Modelling and Analysis Techniques, R. Kiruthika, V. Vardhan and V.S. Vaidyanathan (Eds.), 61-71, Narosa Publishing House, 2016.
• [4] N. Balakrishnan and D. Kundu, Hybrid censoring: Models, inferential results and applications, Comput. Statist. Data Anal. 57 (1), 166-209, 2013.
• [5] R.E. Barlow, A. Madansky, F. Proschan and E.M. Scheuer, Statistical estimation procedures for the burn-in process, Technometrics 10 (1), 51-62, 1968.
• [6] D.J. Bartholomew, The sampling distribution of an estimate arising in life testing, Technometrics 5 (3), 361-374, 1963.
• [7] J.B. Chakrabarty, S. Chowdhury and S. Roy, Optimum reliability acceptance sampling plan using Type-I generalized hybrid censoring scheme for products under warranty, Int. J. Qual. Reliab. Manag. 38 (3), 780-799, 2021.
• [8] J.B. Chakrabarty, S. Roy and S. Chowdhury, On the economic design of optimal sampling plan under accelerated life test setting, Int. J. Qual. Reliab. Manag. 40 (7), 1683-1705, 2023.
• [9] S.M. Chen and G.K. Bhattacharyya, Exact confidence bounds for an exponential parameter under hybrid censoring, Comm. Statist. Theory Methods 16 (8), 2429-2442, 1987.
• [10] J. Chen, W. Chou, H. Wu and H. Zhou, Designing acceptance sampling schemes for life testing with mixed censoring, Nav. Res. Logist. 51 (4), 597-612, 2004.
• [11] L.S. Chen, T. Liang and M.C. Yang, Optimal curtailed Bayesian sampling plans for exponential distributions with Type-I hybrid censored samples, Comm. Statist. Simulation Comput. 50 (3), 764-777, 2021.
• [12] A. Childs, B. Chandrasekar, N. Balakrishnan and D. Kundu, Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution, Ann. Inst. Statist. Math. 55, 319-330, 2003.
• [13] N. Draper and I. Guttman, Bayesian analysis of hybrid life tests with exponential failure times, Ann. Inst. Statist. Math. 39, 219-225, 1987.
• [14] B. Epstein, Truncated life tests in the exponential case, Ann. Inst. Statist. Math. 555-564, 1954.
• [15] K. Fairbanks, R. Madsen and R. Dykstra, A confidence interval for an exponential parameter from a hybrid life test, J. Amer. Statist. Assoc. 77 (377), 137-140, 1982.
• [16] W.T. Huang and Y.P. Lin, Bayesian sampling plans for exponential distribution based on uniform random censored data, Comput. Statist. Data Anal. 44 (4), 669-691, 2004.
• [17] W.T. Huang and Y.P. Lin, An improved Bayesian sampling plan for exponential population with Type-I censoring, Comm. Statist. Theory Methods 31 (11), 2003-2025, 2002.
• [18] N. Khan, G.S. Rao, R.A.K. Sherwani, A.H.Al-Marshadi and M. Aslam, Uncertainty-based sampling plans for various statistical distributions, AIMS Mathematics 8 (6), 14558-14571, 2023.
• [19] M. Kumar and P.C. Ramyamol, Design of optimal reliability acceptance sampling plans for exponential distribution, Econ. Qual. Control 31 (1), 23-36, 2016.
• [20] D. Kundu and R.D. Gupta, Generalized exponential distribution: Bayesian estimations, Comput. Statist. Data Anal. 52 (4), 1873-1883, 2008.
• [21] D. Kundu and B. Pradhan, Estimating the parameters of the generalized exponential distribution in presence of hybrid censoring, Comm. Statist. Theory Methods 38 (12), 2030-2041, 2009.
• [22] C.T. Lin, Y.L. Huang and N. Balakrishnan, Exact Bayesian variable sampling plans for the exponential distribution based on Type-I and Type-II hybrid censored samples, Comm. Statist. Simulation Comput. 37 (6), 1101-1116, 2008.
• [23] Y.P. Lin, T. Liang and W.T. Huang, Bayesian sampling plans for exponential distribution based on Type-I censoring data, Ann. Inst. Statist. Math. 54, 100-113, 2002.
• [24] D.V. Lindley, Approximate Bayesian methods, Trabajos de estadística y de investigación operativa 31, 223-245, 1980.
• [25] MIL-STD-781-C, Reliability design qualification and production acceptance tests: Exponential distribution, US Government Printing Office, Washington, DC, 1977.
• [26] H.A. Noughabi, Testing exponentiality based on the likelihood ratio and power comparison, Ann. Data Sci. textbf2, 195-204, 2015.
• [27] X.Y. Peng and Z. Yan, Bayesian estimation for generalized exponential distribution based on progressive Type-I interval censoring, Acta Math. Appl. Sin. Engl. Ser. 29 (2), 391-402, 2013.
• [28] K. Prajapat, A. Koley, S. Mitra and D. Kundu, An optimal Bayesian sampling plan for two-parameter exponential distribution under Type-I hybrid censoring, Sankhya A, 85 (20), 512-539, 2023.
• [29] D. Prajapati, S. Mitra and D. Kundu, Bayesian sampling plan for the exponential distribution with generalized Type-I hybrid censoring scheme, J. Stat. Theory Pract. 17 (1), 5, 2023.
• [30] D. Prajapati, S. Mitra and D. Kundu, Bayesian sampling plan for the exponential distribution with generalized Type-II hybrid censoring scheme, Comm. Statist. Simulation Comput. 52 (2), 533-556, 2023.
• [31] D. Prajapati, S. Mitra, D. Kundu and A. Pal, Optimal Bayesian sampling plan for censored competing risks data, J. Stat. Comput. Simul. 93 (5), 775-799, 2022.
• [32] K.S.N. Sharma, Design of multiple deferred state repetitive group sampling plans for life tests based on generalized gamma distribution, Qual. Eng. 35 (2), 248-257, 2023.
• [33] R.E. Sherman, Design and evaluation of a repetitive group sampling plan, Technometrics 7 (1), 11-21, 1965.
• [34] L. Yeh, Bayesian variable sampling plans for the exponential distribution with Type-I censoring, Ann. Statist. 696-711, 1994.
• [35] L. Yeh and S.T.B. Choy, Bayesian variable sampling plans for the exponential distribution with uniformly distributed random censoring, J. Statist. Plann. Inference 47 (3), 277-293, 1995.